August 31, 2009
Are the new rules of logic upon which computation can be based, radically different from conventional logic? Alternatively, is it an extension of conventional logic + something else?
Computation is ultimately about following rules—of any kind. Traditional logic represents just one class of rules. There are lots of others that can be used. One of the surprising discoveries from NKS is just how easy it is to find rules that can support universal computation. And that’s important if one wants to base computation on elements like molecules. About logic itself: I wondered just how special the axiom system of logic that we use is. One can enumerate the whole space of possible axiom systems, and then one finds that logic is about the 50,000 system one encounters. There’s really nothing special about it, except the role it plays in human intellectual history.